Estimate the magnitude of the electric field strength due to the proton in a hydrogen atom at a distance of 5.29x10^-11 m, the expected position of the electron in the atom.
5.17 x 10^11
To estimate the magnitude of the electric field strength due to the proton in a hydrogen atom at a given distance, you need to use Coulomb's Law.
Coulomb's Law states that the electric field strength (E) between two charged particles is directly proportional to the product of their charges (q1 and q2) and inversely proportional to the square of the distance (r) between them:
E = k * (q1 * q2) / r^2
Where:
E = Electric field strength
k = Coulomb's constant (9 x 10^9 N m^2 / C^2)
q1 = Charge of the first particle
q2 = Charge of the second particle
r = Distance between the particles
In a hydrogen atom, the proton carries a charge of +1.6 x 10^-19 C. Hence, we can estimate the electric field strength due to the proton at a distance of 5.29 x 10^-11 m, the expected position of the electron in the atom.
Plugging the values into the formula:
E = (9 x 10^9 N m^2 / C^2) * [ (+1.6 x 10^-19 C) * (+1.6 x 10^-19 C) ] / (5.29 x 10^-11 m)^2
Simplifying the equation:
E = (9 x 10^9 N m^2 / C^2) * (2.56 x 10^-38 C^2) / (2.796 x 10^-21 m^2)
E = 2.1 x 10^8 N/C
Therefore, the magnitude of the electric field strength due to the proton in a hydrogen atom at a distance of 5.29 x 10^-11 m is approximately 2.1 x 10^8 N/C.
Force=kqq/r^2
E=ke/r^2